This invention relates to the computation of differential azimuth between two sets of spaced-apart gravity component measurement devices in a borehole, subject to the constraint that there is no rotation about the borehole axis between the two sets of measuring devices, generally known as accelerometers. Such a structure cannot determine absolute azimuth orientation but only the differential azimuth between the two spaced-apart sets of gravity component measurements. Such apparatus in general is referenced in prior art U.S. patent application Ser. No. 06/200,096, Borehole Survey Apparatus and Method, filed Oct. 23, 1980, describing one such a mechanization. That application was processed to the point of allowance of all claims and then abandoned. Another prior art example is described in U.S. Pat. No. 6,480,119, Surveying a Subterranean Borehole Using Accelerometers, issued Nov. 12, 2002. No details are there provided on the development of the equation shown therein for differential azimuth and there are issues with that equation that lead to a conclusion that acceptable results are not consistently obtainable for all possible input conditions.
It is an objective of the present invention to provide a preferred method for obtaining the above cited differential azimuth measurement that is completely described so as to teach and show the method and to provide an improved method verifiable as correct by independent analysis by users. Further, it is an objective to provide two alternative embodiments that are simpler computationally, but demonstrate less geometrical accuracy than the preferred method. These two alternatives are similarly completely described.